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Symmetry, Integrability and Geometry: Methods and Applications, 2008, Volume 4, 069, 33 pp.
DOI: https://doi.org/10.3842/SIGMA.2008.069 (Mi sigma322) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Homogeneous Poisson Structures on Loop Spaces of Symmetric Spaces

Doug Pickrell

Department of Mathematics, University of Arizona, Tucson, AZ, 85721, USA
Full-text PDF (396 kB) Citations (5)
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DOI: https://doi.org/10.3842/SIGMA.2008.069
Abstract: This paper is a sequel to [Caine A., Pickrell D., Int. Math. Res. Not., to appear, arXiv:0710.4484], where we studied the Hamiltonian systems which arise from the Evens–Lu construction of homogeneous Poisson structures on both compact and noncompact type symmetric spaces. In this paper we consider loop space analogues. Many of the results extend in a relatively routine way to the loop space setting, but new issues emerge. The main point of this paper is to spell out the meaning of the results, especially in the $SU(2)$ case. Applications include integral formulas and factorizations for Toeplitz determinants.
Keywords: Poisson structure; loop space; symmetric space; Toeplitz determinant.
Received: June 14, 2008; in final form September 27, 2008; Published online October 7, 2008
Bibliographic databases:
Document Type: Article
MSC: 22E67; 53D17; 53D20
Language: English
Citation: Doug Pickrell, “Homogeneous Poisson Structures on Loop Spaces of Symmetric Spaces”, SIGMA, 4 (2008), 069, 33 pp.
Citation in format AMSBIB
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